Question

a 3.0m beam with a mas of 130kg is supported at each end. a 70kg student stands 2.0m from support, how much upward force does each support exert on the beam?

Answer 1

Question:

a 3.0m beam with a mas of $130\mathrm{kg}$ is supported at each end. a $70\mathrm{kg}$ student stands $2.0\mathrm{m}$ from support, how much upward force does each support exert on the beam?

Solution:

$\mathsf{L} = 3.0\mathsf{m}$ - the lengths of beam;

$\mathsf{M} = 130\mathsf{kg}$ - the mass of beam.

$\mathsf{m} = 70\mathsf{kg}$ - the mass of student

$\mathsf{g} = 10\frac{\mathsf{m}}{\mathsf{s}^2}$

$\vec{F_1}, \vec{F_2}$ - upward forces;

First Newton's law of motion:

$$F _ {1} + F _ {2} = m g + M g$$ $$m g \cdot \frac {L}{3} + M g \cdot \frac {L}{2} - F _ {2} \cdot L = 0$$ $$m g \cdot \frac {1}{3} + M g \cdot \frac {1}{2} = F _ {2} = 7 0 \cdot 1 0 \frac {1}{3} + 1 3 0 \cdot 1 0 \frac {1}{2} \approx 2 3 3 + 6 5 0 = 8 8 3 N$$ $$F _ {1} + m g \cdot \frac {1}{3} + M g \cdot \frac {1}{2} = m g + M g$$ $$F _ {1} = m g \cdot \frac {2}{3} + M g \cdot \frac {1}{2} = 7 0 \cdot 1 0 \frac {2}{3} + 1 3 0 \cdot 1 0 \frac {1}{2} \approx 4 6 7 + 6 5 0 = 1 1 1 7 N$$